The name of the State is Éire, or, in the English language, Ireland.
Nó i nGaeilge:
Is Stát ceannasach, neamhspleách, daonlathach Éire.
The description "Republic of Ireland" is just that, a description and not a name. It is provided for in the Republic of Ireland Act (1948) but it does not replace or supplant the official name of the state. Within the context of politics there is a small likelihood of the tag being confused with questions referring instead to the island of Ireland and these issues can be addressed through editing. Whilst we're at it adding the Synonyms "republic-of-Ireland" and "Éire".